{
  "id": "1105.4453",
  "version": "v1",
  "published": "2011-05-23T10:00:13.000Z",
  "updated": "2011-05-23T10:00:13.000Z",
  "title": "Saturating Sperner families",
  "authors": [
    "Dániel Gerbner",
    "Balázs Keszegh",
    "Nathan Lemons",
    "Dömötör Pálvölgyi",
    "Cory Palmer",
    "Balázs Patkós"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A family $\\cF \\subseteq 2^{[n]}$ saturates the monotone decreasing property $\\cP$ if $\\cF$ satisfies $\\cP$ and one cannot add any set to $\\cF$ such that property $\\cP$ is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the $k$-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of $l$-sets and $(l+1)$-sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-23T10:00:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "saturating sperner families",
      "sperner property",
      "monotone decreasing property",
      "minimum size"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.4453G"
    }
  }
}